Organopolysiloxanes are used in various industrial fields such as electric, electrical, automobile, office automation equipment, medical care, cosmetic, food, and architecture industries. According to requirements and usages in each of the fields, organopolysiloxanes having various kinds of organic substituent groups have been developed. An organopolysiloxane having a carboxyl group or its salts, hereinafter collectively referred to as “carboxyl group”, has been also developed for the reason that the carboxyl group is useful for surface-treating fibers, paper, human hair and inorganic fillers because of its functionalities such as reactivity and electrolytic property.
For example, an organopolysiloxanes having the following carboxyl group is known.

WO 96/32432 A1 describes an organopolysiloxane having the following group:

JP 2002-114849A describes an organopolysiloxane having either of the following groups:
wherein X is —O— or —NH—, M is a hydrogen atom, metal, ammonium or the like.
U.S. Pat. No 6,592,854 B1 describes an organopolysiloxane having the following groups:—(R1O)a—R2—(OR3)b—COOMwherein M is a hydrogen atom, alkali metal, ammonium or the like.
WO 03/095530 A1 and WO 03/094871 A1 describe an organopolysiloxane having the following group:

In the above organopolysiloxanes, the first three organopolysiloxanes have only one carboxyl group bonded to a silicon atom. The fourth organopolysiloxane has two carboxyl groups per silicon atom. However, it has a drawback that it has to be prepared from a special organopolysiloxane having two terminal amino groups or a special organopolysiloxane having an amino group and a hydroxyl group. The fifth organopolysiloxane is relatively easy to prepare. However, its affinity with unctuous agents such as hydrocarbon unctuous agent is not satisfactory.